The general solution fo `(dy)/(dx) = (ax +h)/(by +h) ` represents a circle only when

Options

A. a=b=0
B. ` a= -b ne 0`
C. ` a= bne 0, h =k`
D. ` a = bne 0`

Answer

B

Explanation

`(dy)/(dx)= (ax +h)/(by +k)`
` Rightarrow (by+ k) dy = (ax +h) dx`
Intergrating,we get ` int (by + k) dy = int (ax+h) dx`
` Rightarrow (by^(2))/2 + ky = (ax^(2))/2 + hx`
` Rightarrow ax^(2) -by^(2) =ax^(2) -2ky =0`
This repesents circle only when ` a = -b ne 0` .